(1-z)(4z-6)=0

Solution for (1-z)(4z-6)=0 equation:

Simplifying
(1 + -1z)(4z + -6) = 0

Reorder the terms:
(1 + -1z)(-6 + 4z) = 0

Multiply (1 + -1z) * (-6 + 4z)
(1(-6 + 4z) + -1z * (-6 + 4z)) = 0
((-6 * 1 + 4z * 1) + -1z * (-6 + 4z)) = 0
((-6 + 4z) + -1z * (-6 + 4z)) = 0
(-6 + 4z + (-6 * -1z + 4z * -1z)) = 0
(-6 + 4z + (6z + -4z2)) = 0

Combine like terms: 4z + 6z = 10z
(-6 + 10z + -4z2) = 0

Solving
-6 + 10z + -4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 5z + -2z2) = 0

Factor a trinomial.
2((-3 + 2z)(1 + -1z)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 2z)' equal to zero and attempt to solve:

Simplifying
-3 + 2z = 0

Solving
-3 + 2z = 0

Move all terms containing z to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + 2z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2z = 0 + 3
2z = 0 + 3

Combine like terms: 0 + 3 = 3
2z = 3

Divide each side by '2'.
z = 1.5

Simplifying
z = 1.5
Subproblem 2
Set the factor '(1 + -1z)' equal to zero and attempt to solve:

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1z = 0 + -1
-1z = 0 + -1

Combine like terms: 0 + -1 = -1
-1z = -1

Divide each side by '-1'.
z = 1

Simplifying
z = 1
Solution
z = {1.5, 1}